In the context of our benchmark scenario in this section, we shall assume that the helicity stored in the hypermagnetic field survives and the field itself remains fully helical all the way down to the EWPT.\(14\endcsname \)If the hypermagnetic field is only partially helical, its coherence length and field strength at a fixed value of the total helicity are larger than in the fully helical case.
This results in large baryon isocurvature perturbations and hence severe constraints from inhomogeneous big-bang nucleosynthesis [1]}.
In the parameter space of our interest, the hypermagnetic field is, however, in the turbulent regime and its coherence length is sufficiently short so that no constraint from baryon isocurvature perturbations arises.

The necessary conditions for this to happen were outlined in Sec. ; in Sec. REF , we will identify the viable region in the parameter space of axion inflation where these conditions are indeed satisfied.
For the time being, let us, however, solely focus on the implications for the BAU if the primordial helicity of the gauge field is not erased before the EWPT.
The crucial observation in this case is that the decay of the hypermagnetic helicity during the EWPT will result in another contribution to the baryon asymmetry in accord with the chiral anomaly of the baryon-number current in Eq. (REF ) and the relation among the involved global charges in Eq. (REF ).
We refer to this mechanism as baryogenesis from helicity decay, which has been first proposed in Refs. [2]}, [3]} and then studied in more detail in Refs. [4]}, [5]}, [6]} as well as in Refs. [7]}, [8]}, [9]} in relation to axion inflation.
